Restoring the Bloch-Nordsieck theorem in the electroweak sector of the standard model

Abstract

The electroweak gauge symmetry cannot be broken in a literal sense due to Elitzur's theorem. Thus, asymptotic states need to be manifestly and non-perturbatively gauge-invariant with respect to the electroweak symmetry. To take this suitably into account perturbation theory augmented by the Fr\"ohlich-Morchio-Strocchi mechanism can be used. We show that this restores the Bloch-Nordsieck theorem in electroweak processes in the standard model. This has potentially substantial impact at, e.g., future lepton colliders, but has only negligible effects at lower energies. We also demonstrate an alternative implementation using PDFs, which allows an approach with manifest electroweak Bloch-Nordsieck theorem also at hadron colliders.